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CoUrSe ModUle SUMMary and UnpaCkIng of StandardS | 75Solve equations and inequalities in one variable.
A-REI.B.3 Solve linear equations and inequalities in one variable, including equations with
coefficients represented by letters.
Solve systems of equations.
A-REI.C.6^18 Solve systems of linear equations exactly and approximately (e.g., with graphs),
focusing on pairs of linear equations in two variables.
Represent and solve equations and inequalities graphically.
A-REI.D.10 Understand that the graph of an equation in two variables is the set of all its
solutions plotted in the coordinate plane, often forming a curve (which could be a line).
Focus standaRds FoR MatheMatical pRactice
MP.1 Make sense of problems and persevere in solving them. Students are presented with
problems that require them to try special cases and simpler forms of the original problem to
gain insight into the problem.
MP.2 Reason abstractly and quantitatively. Students analyze graphs of non-constant rate
measurements and apply reason (from the shape of the graphs) to infer the quantities being
displayed and consider possible units to represent those quantities.
MP.4 Model with mathematics. Students have numerous opportunities to solve problems
that arise in everyday life, society, and the workplace (e.g., modeling bacteria growth and
understanding the federal progressive income tax system).
MP.7 Look for and make use of structure. Students reason with and analyze collections of
equivalent expressions to see how they are linked through the properties of operations. They
discern patterns in sequences of solving equation problems that reveal structures in the
equations themselves (e.g., 24 x+= 10 , 23 ()x-+ 41 = 0 , 23 ()x-+ 44 = 10 ).
MP.8 Look for and express regularity in repeated reasoning. After solving many linear
equations in one variable (e.g., 3 xx+= 58 - 17 ), students look for general methods for
solving a generic linear equation in one variable by replacing the numbers with letters (e.g.,
ax+=bcxd+ ). They pay close attention to calculations involving the properties of operations,
properties of equality, and properties of inequalities, to find equivalent expressions and solve
equations, while recognizing common ways to solve different types of equations.
Module topic suMMaRies
Topic A: Linear and Exponential Sequences
In Lesson 1 of Topic A, students challenge the idea that patterns can be defined by merely
seeing the first few numbers of the pattern. They learn that a sequence is an ordered list of
elements and that it is sometimes intuitive to number the elements in a sequence beginning
with 0 rather than 1. In Lessons 2 and 3, students learn to define sequences explicitly and
recursively and begin their study of arithmetic and geometric sequences that continues
through Lessons 4–7 as students explore applications of geometric sequences. In the final
lesson, students compare arithmetic and geometric sequences as they compare growth rates.